Hydrodynamic Problems Solved by Rheoelectric Analogies 



considerable improvement of its efficiency in performing the functions required 

 of it. 



To conduct this study, we are obliged to admit certain hypotheses. We shall 

 assume that: the downstream flow is made axial by straighteners, the propeller 

 is approximated by an actuator disc (infinite-number-of-blades hypothesis) with 

 a discontinuity of constant pressure during its passage (constant circulation 

 hypothesis). Consequently the flow is axisymmetric and its study can be limited 

 to a demiplan meridian. Although this first simplification is necessary, it is not 

 ultimately sufficient, because if we are to represent the flow correctly we must 

 know the discontinuity surface of the velocities which escapes from the trailing 

 edge of the duct; i.e., we must know the free-boundary-with-equilibrium condition 

 which imposes equality between the pressure jump and the difference of the 

 square of the velocities on each side of the Jetstream. The difficulty in repre- 

 senting such a condition requires the use of a linearized schema wherein the 

 boundary conditions are imposed on a straight semi-indefined cylinder of gen- 

 erators parallel to the unperturbed velocity, and on an image of the duct and 

 of the discontinuity surface. The flow can then be defined by means of the 

 perturbation-velocities-potential harmonic revolution function, which is easily 

 represented by the electric potential of a tank with an inclined bottom. 



Because of the many conditions which must be satisfied in order to improve 

 the hydrodynamic functioning and efficiency of the nozzle, it seemed useful to 

 take as a starting point a given duct form, which is then redefined during the 

 calculation on the basis of the results obtained. The process is greatly facilitated 

 by consideration of several elementary potentials which have in the past revealed 

 the interactions of the propeller and hub on the duct. 



This method permits us to show the role played in the increasing of effi- 

 ciency by two effects; the downstream divergence of the mean line of the duct in 

 connection with the increase of velocity in the plane of the actuator disc, which 

 facilitates and improves the functioning of the latter; and the "adaptation" con- 

 dition, imposed during the design on the nose of the duct, which reduces the 

 risks of flow separation on the inner surface of the nozzle, and consequently en- 

 courages its efficiency, as well as that of the propeller. We must point out 

 nevertheless that the widening effect of the nozzle can be obtained by the blowing 

 effect on the trailing edge, an effect also studied by rheoelectric analogy by 

 means of analog hypotheses (11). .. •.. 



This method has been used for the calculation of a combined propeller- 

 rectifier- nozzle with the following characteristics: 



Thrust T = 19,000 Kgr 



Diameter of the propeller D = 2.58 m 



Length of the nozzle L = 1.87 m 



Advance coefficient A = Vg/nD = 0.696 



Thrust coefficient K^ = T/pn^B'* = 0.258, 



405 



